There are several synonyms for the colloquial phrase "bite someone's head off" that can be used to convey a similar meaning without the aggressive connotation. One alternative is "snap at" which implies a quick and sharp retort. Another option is "lash out" which suggests a sudden angry response to a comment or situation. "Fly off the handle" is a phrase often used to describe someone who becomes enraged quickly and without warning. Additionally, "blow up" or "lose one's temper" can be used to describe a more explosive reaction. It's important to choose the appropriate synonym based on the context of the conversation and the level of emotion being conveyed.